Zhimin Hu and Stephan T. Grilli
Postdoctoral Res. Associate Associate
Professor
Department of Ocean Engng.
niversity of Rhode Island
Narragansett, RI 02882, USA
Abstract :
A new model is proposed to compute the time evolution of the
interface between two inviscid fluids moving with uniform velocity, subjected
to instabilities of the Kelvin-Helmholtz (KH) type. In this model, the
interface is represented by a Continuous Vortex Sheet (CVS) which both
preserves the full nonlinearity of interfacial boundary conditions and
provides a higher-order representation of the geometry and field variables
than in previously proposed models. Time updating of CVS's geometry and
circulation is calculated as a function of gravity, interfacial surface
tension, and fluid density difference. An intrinsic variable expansion
technique is introduced to deal with the hyper-singularity occurring in
the Biot-Savart integrals describing CVS's velocity. The model is applied
to predict the nonlinear growth of periodic KH instabilities in a two fluid
stratified system. Results demonstrate that the CVS representation provides
both higher numerical accuracy and stability and gives a more accurate
physical picture of the disturbance evolution than less accurate methods,
like point vortex models, used in earlier analyses.
Keywords :
Continuous vortex sheet, stratified fluid instability, KH instability